locally finite p-groups with all subgroups either subnormal or nilpotent-by-chernikov

‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in which all subgroups are either subnormal or‎ ‎nilpotent-by-chernikov‎. ‎denoting by $mathfrak{x}$ the class of all such‎ ‎groups‎, ‎our concern here is with locally finite p-groups in the class‎ ‎$mathfrak{x}$‎, ‎where $p$ is a prime‎, ‎while an earlier article provided a‎ ‎reasonable classification of locally finite $mathfrak{x}$nb-groups in which‎ ‎all of the p-sections are nilpotent-by-chernikov‎. ‎our main result is that‎ ‎if $g$ is a baer p-group in $mathfrak{x}$ then $g$ is nilpotent-by-chernikov‎ .